Simplify the expression. Write your answer as a power. $$ \begin{array}{ll} ext { A. } 4 \cdot 4^{5}=4^{6} & ext { B. } 6^{3} \cdot 6^{7} \ ext { C. }(-3)^{8} \cdot(-3)^{3} & ext { D. }\left(\frac{4}{5} ight)^{2} \cdot\left(\frac{4}{5} ight)^{6} \ ext { E. }\left(7^{3} ight)^{5} & ext { F. }\left((-8)^{10} ight)^{3} \ ext { Simplify the expression. } \ ext { G. }(8 a)^{3} & ext { H. }(-4 c)^{5} \ ext { I. }(1.5 r)^{2} & ext { J. }\left(\frac{2}{3} m ight)^{4} \ ext { K. } 3^{2} \cdot 3^{4}-4^{4} & ext { L. } 7 \cdot\left(7^{3}-7^{2} ight) \ ext { M. }\left(\frac{1}{3} ight)^{4} \cdot\left(9^{3} ight)^{2} & \begin{array}{l} ext { N. The budget for a remake of a movie is } 100 ext { times the } \ ext { budget of the original movie. The original movie's } \ ext { budget was } 10^{5} ext { dollars. What is the budget of the } \ ext { remake? Express your answer as a power. }\end{array}\end{array}{ }_{l} $$

Question

Simplify the expression. Write your answer as a power. $$ \begin{array}{ll}	ext { A. } 4 \cdot 4^{5}=4^{6} & 	ext { B. } 6^{3} \cdot 6^{7} \ 	ext { C. }(-3)^{8} \cdot(-3)^{3} & 	ext { D. }\left(\frac{4}{5}ight)^{2} \cdot\left(\frac{4}{5}ight)^{6} \ 	ext { E. }\left(7^{3}ight)^{5} & 	ext { F. }\left((-8)^{10}ight)^{3} \ 	ext { Simplify the expression. } \ 	ext { G. }(8 a)^{3} & 	ext { H. }(-4 c)^{5} \ 	ext { I. }(1.5 r)^{2} & 	ext { J. }\left(\frac{2}{3} might)^{4} \ 	ext { K. } 3^{2} \cdot 3^{4}-4^{4} & 	ext { L. } 7 \cdot\left(7^{3}-7^{2}ight) \ 	ext { M. }\left(\frac{1}{3}ight)^{4} \cdot\left(9^{3}ight)^{2} & \begin{array}{l}	ext { N. The budget for a remake of a movie is } 100 	ext { times the } \ 	ext { budget of the original movie. The original movie's } \ 	ext { budget was } 10^{5} 	ext { dollars. What is the budget of the } \ 	ext { remake? Express your answer as a power. }\end{array}\end{array}{ }_{l} $$

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$6^{3}\times 6^{7}$$
- step1: Multiply:
  $$6^{3+7}$$
- step2: Add the numbers:
  $$6^{10}$$
Calculate or simplify the expression $$ 100 * 10^5 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$100\times 10^{5}$$
- step1: Rewrite the expression:
  $$10^{2}\times 10^{5}$$
- step2: Rewrite the expression:
  $$10^{2+5}$$
- step3: Calculate:
  $$10^{7}$$
Calculate or simplify the expression $$ (4/5)^2 * (4/5)^6 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{4}{5}\right)^{2}\left(\frac{4}{5}\right)^{6}$$
- step1: Multiply:
  $$\left(\frac{4}{5}\right)^{2+6}$$
- step2: Add the numbers:
  $$\left(\frac{4}{5}\right)^{8}$$
- step3: Simplify:
  $$\frac{4^{8}}{5^{8}}$$
- step4: Evaluate the power:
  $$\frac{65536}{5^{8}}$$
Calculate or simplify the expression $$ (1.5*r)^2 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(1.5r\right)^{2}$$
- step1: Convert the expressions:
  $$\left(\frac{3}{2}r\right)^{2}$$
- step2: Use the properties of exponents:
  $$\left(\frac{3}{2}\right)^{2}r^{2}$$
- step3: Evaluate the power:
  $$\frac{9}{4}r^{2}$$
Calculate or simplify the expression $$ (7^3)^5 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(7^{3}\right)^{5}$$
- step1: Multiply the exponents:
  $$7^{3\times 5}$$
- step2: Multiply the numbers:
  $$7^{15}$$
Calculate or simplify the expression $$ ((-8)^10)^3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\left(-8\right)^{10}\right)^{3}$$
- step1: Multiply the exponents:
  $$\left(-8\right)^{10\times 3}$$
- step2: Multiply the numbers:
  $$\left(-8\right)^{30}$$
- step3: Determine the sign:
  $$8^{30}$$
Calculate or simplify the expression $$ (8*a)^3 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(8a\right)^{3}$$
- step1: Use the properties of exponents:
  $$8^{3}a^{3}$$
- step2: Evaluate the power:
  $$512a^{3}$$
Calculate or simplify the expression $$ (-4*c)^5 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(-4c\right)^{5}$$
- step1: Determine the sign:
  $$-\left(4c\right)^{5}$$
- step2: Use the properties of exponents:
  $$-4^{5}c^{5}$$
- step3: Evaluate the power:
  $$-1024c^{5}$$
Calculate or simplify the expression $$ (-3)^8 * (-3)^3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(-3\right)^{8}\left(-3\right)^{3}$$
- step1: Multiply:
  $$\left(-3\right)^{8+3}$$
- step2: Add the numbers:
  $$\left(-3\right)^{11}$$
- step3: Determine the sign:
  $$-3^{11}$$
Calculate or simplify the expression $$ 4 * 4^5 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$4\times 4^{5}$$
- step1: Calculate:
  $$4^{6}$$
- step2: Evaluate the power:
  $$4096$$
Calculate or simplify the expression $$ 3^2 * 3^4 - 4^4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$3^{2}\times 3^{4}-4^{4}$$
- step1: Multiply the numbers:
  $$3^{6}-4^{4}$$
- step2: Evaluate the power:
  $$729-4^{4}$$
- step3: Evaluate the power:
  $$729-256$$
- step4: Subtract the numbers:
  $$473$$
Calculate or simplify the expression $$ 7*(7^3 - 7^2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$7\left(7^{3}-7^{2}\right)$$
- step1: Subtract the numbers:
  $$7\times 294$$
- step2: Multiply the numbers:
  $$2058$$
Calculate or simplify the expression $$ (2/3*m)^4 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(\frac{2}{3}m\right)^{4}$$
- step1: Use the properties of exponents:
  $$\left(\frac{2}{3}\right)^{4}m^{4}$$
- step2: Evaluate the power:
  $$\frac{16}{81}m^{4}$$
Calculate or simplify the expression $$ (1/3)^4 * (9^3)^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{1}{3}\right)^{4}\left(9^{3}\right)^{2}$$
- step1: Multiply the exponents:
  $$\left(\frac{1}{3}\right)^{4}\times 9^{3\times 2}$$
- step2: Multiply the numbers:
  $$\left(\frac{1}{3}\right)^{4}\times 9^{6}$$
- step3: Rewrite the expression:
  $$\left(\frac{1}{3}\right)^{4}\left(\frac{1}{3}\right)^{-12}$$
- step4: Simplify:
  $$\left(\frac{1}{3}\right)^{-8}$$
- step5: Simplify:
  $$3^{8}$$
- step6: Evaluate the power:
  $$6561$$
Let's simplify each expression step by step:

### A. $$ 4 \cdot 4^{5} $$
Using the property of exponents $$ a^m \cdot a^n = a^{m+n} $$:
$$
4 \cdot 4^{5} = 4^{1+5} = 4^{6}
$$

### B. $$ 6^{3} \cdot 6^{7} $$
Using the same property:
$$
6^{3} \cdot 6^{7} = 6^{3+7} = 6^{10}
$$

### C. $$ (-3)^{8} \cdot (-3)^{3} $$
Again, applying the property:
$$
(-3)^{8} \cdot (-3)^{3} = (-3)^{8+3} = (-3)^{11}
$$

### D. $$ \left(\frac{4}{5}\right)^{2} \cdot \left(\frac{4}{5}\right)^{6} $$
Using the property:
$$
\left(\frac{4}{5}\right)^{2} \cdot \left(\frac{4}{5}\right)^{6} = \left(\frac{4}{5}\right)^{2+6} = \left(\frac{4}{5}\right)^{8}
$$

### E. $$ \left(7^{3}\right)^{5} $$
Using the power of a power property $$ (a^m)^n = a^{m \cdot n} $$:
$$
\left(7^{3}\right)^{5} = 7^{3 \cdot 5} = 7^{15}
$$

### F. $$ \left((-8)^{10}\right)^{3} $$
Using the power of a power property:
$$
\left((-8)^{10}\right)^{3} = (-8)^{10 \cdot 3} = (-8)^{30}
$$

### G. $$ (8a)^{3} $$
Using the power of a product property $$ (ab)^n = a^n b^n $$:
$$
(8a)^{3} = 8^{3} a^{3} = 512a^{3}
$$

### H. $$ (-4c)^{5} $$
Using the same property:
$$
(-4c)^{5} = (-4)^{5} c^{5} = -1024c^{5}
$$

### I. $$ (1.5r)^{2} $$
Using the power of a product property:
$$
(1.5r)^{2} = (1.5)^{2} r^{2} = \frac{9}{4}r^{2}
$$

### J. $$ \left(\frac{2}{3} m\right)^{4} $$
Using the power of a product property:
$$
\left(\frac{2}{3} m\right)^{4} = \left(\frac{2}{3}\right)^{4} m^{4} = \frac{16}{81}m^{4}
$$

### K. $$ 3^{2} \cdot 3^{4} - 4^{4} $$
First, simplify $$ 3^{2} \cdot 3^{4} $$:
$$
3^{2} \cdot 3^{4} = 3^{6}
$$
Now calculate $$ 4^{4} = 256 $$:
$$
3^{6} - 256 = 729 - 256 = 473
$$

### L. $$ 7 \cdot (7^{3} - 7^{2}) $$
First, simplify inside the parentheses:
$$
7^{3} - 7^{2} = 7^{2}(7 - 1) = 7^{2} \cdot 6
$$
Now multiply:
$$
7 \cdot 7^{2} \cdot 6 = 7^{3} \cdot 6 = 42 \cdot 7^{3} = 2058
$$

### M. $$ \left(\frac{1}{3}\right)^{4} \cdot \left(9^{3}\right)^{2} $$
First, simplify $$ 9^{3} = (3^{2})^{3} = 3^{6} $$:
$$
\left(9^{3}\right)^{2} = (3^{6})^{2} = 3^{12}
$$
Now combine:
$$
\left(\frac{1}{3}\right)^{4} \cdot 3^{12} = 3^{-4} \cdot 3^{12} = 3^{12-4} = 3^{8}
$$

### N. Budget for a remake
The budget for the remake is $$ 100 \times 10^{5} = 10^{2} \times 10^{5} = 10^{7} $$.

### Summary of Results
- A: $$ 4^{6} $$
- B: $$ 6^{10} $$
- C: $$ (-3)^{11} $$
- D: $$ \left(\frac{4}{5}\right)^{8} $$
- E: $$ 7^{15} $$
- F: $$ (-8)^{30} $$
- G: $$ 512a^{3} $$
- H: $$ -1024c^{5} $$
- I: $$ \frac{9}{4}r^{2} $$
- J: $$ \frac{16}{81}m^{4} $$
- K: $$ 473 $$
- L: $$ 2058 $$
- M: $$ 3^{8} $$
- N: $$ 10^{7} $$
A: $$4^{6}$$, B: $$6^{10}$$, C: $$(-3)^{11}$$, D: $$\left(\frac{4}{5}\right)^{8}$$, E: $$7^{15}$$, F: $$(-8)^{30}$$, G: $$512a^{3}$$, H: $$-1024c^{5}$$, I: $$\frac{9}{4}r^{2}$$, J: $$\frac{16}{81}m^{4}$$, K: $$473$$, L: $$2058$$, M: $$3^{8}$$, N: $$10^{7}$$.

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