A. $$ 1 \frac{2}{3}: 2 \frac{3}{3} $$ 4.2. $$ 2(\sqrt[3]{64}+\sqrt{25}) $$ 4.3. $$ \left(\frac{64}{125}\right)^{x}=\left(\frac{5}{4}\right)^{-x} \quad \operatorname{sit}-x+x $$ 4. $$ \quad 99 x^{2}+(5 x)^{0}= $$ $$ 7 \frac{3^{10} \times 2^{4}}{3^{6} \times 2^{6}} $$ 4 S. Simpl-fy $$ \frac{16 x 1^{3} \times\left(x^{3} 1\right)^{4}}{\left(2 x^{4} 1^{4}\right)^{3}} $$

Question

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Solution:
  $$99x^{2}+\left(5x\right)^{0}$$
- step1: Rewrite the expression:
  $$99x^{2}+1$$
Solve the equation $$ (\frac{64}{125})^{x}=(\frac{5}{4})^{-x} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\left(\frac{64}{125}\right)^{x}=\left(\frac{5}{4}\right)^{-x}$$
- step1: Rewrite the expression:
  $$\left(\frac{5}{4}\right)^{-3x}=\left(\frac{5}{4}\right)^{-x}$$
- step2: Set the exponents equal:
  $$-3x=-x$$
- step3: Add or subtract both sides:
  $$-3x-\left(-x\right)=0$$
- step4: Subtract the terms:
  $$-2x=0$$
- step5: Change the signs:
  $$2x=0$$
- step6: Rewrite the expression:
  $$x=0$$
Calculate or simplify the expression $$ \frac{16*x*1^{3}*(x^{3}*1)^{4}}{(2*x^{4}*1^{4})^{3}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{16x\times 1^{3}\times \left(x^{3}\times 1\right)^{4}}{\left(2x^{4}\times 1^{4}\right)^{3}}$$
- step1: Multiply:
  $$\frac{16x\times 1^{3}\times \left(x^{3}\right)^{4}}{\left(2x^{4}\times 1^{4}\right)^{3}}$$
- step2: Evaluate the power:
  $$\frac{16x\times 1^{3}\times \left(x^{3}\right)^{4}}{\left(2x^{4}\times 1\right)^{3}}$$
- step3: Multiply the terms:
  $$\frac{16x\times 1^{3}\times \left(x^{3}\right)^{4}}{\left(2x^{4}\right)^{3}}$$
- step4: Evaluate the power:
  $$\frac{16x\times 1\times \left(x^{3}\right)^{4}}{\left(2x^{4}\right)^{3}}$$
- step5: Evaluate the power:
  $$\frac{16x\times 1\times x^{12}}{\left(2x^{4}\right)^{3}}$$
- step6: Calculate:
  $$\frac{16x\times x^{12}}{\left(2x^{4}\right)^{3}}$$
- step7: Multiply:
  $$\frac{16x^{13}}{\left(2x^{4}\right)^{3}}$$
- step8: Factor the expression:
  $$\frac{16x^{13}}{8x^{12}}$$
- step9: Reduce the fraction:
  $$2x$$
Calculate or simplify the expression $$ 1 + \frac{2}{3} : 2 + \frac{3}{3} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$1+\frac{2}{3}\div 2+\frac{3}{3}$$
- step1: Divide the terms:
  $$1+\frac{2}{3}\div 2+1$$
- step2: Divide the terms:
  $$1+\frac{1}{3}+1$$
- step3: Add the numbers:
  $$2+\frac{1}{3}$$
- step4: Reduce fractions to a common denominator:
  $$\frac{2\times 3}{3}+\frac{1}{3}$$
- step5: Transform the expression:
  $$\frac{2\times 3+1}{3}$$
- step6: Multiply the numbers:
  $$\frac{6+1}{3}$$
- step7: Add the numbers:
  $$\frac{7}{3}$$
Calculate or simplify the expression $$ 7*(\frac{3^{10}*2^{4}}{3^{6}*2^{6}}) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$7\left(\frac{3^{10}\times 2^{4}}{3^{6}\times 2^{6}}\right)$$
- step1: Multiply by $$a^{-n}:$$
  $$7\times 3^{10}\times 2^{4}\times 3^{-6}\times 2^{-6}$$
- step2: Multiply the terms:
  $$7\times 3^{10-6}\times 2^{4}\times 2^{-6}$$
- step3: Subtract the numbers:
  $$7\times 3^{4}\times 2^{4}\times 2^{-6}$$
- step4: Multiply the terms:
  $$7\times 3^{4}\times 2^{4-6}$$
- step5: Subtract the numbers:
  $$7\times 3^{4}\times 2^{-2}$$
- step6: Multiply the terms:
  $$567\times 2^{-2}$$
- step7: Evaluate the power:
  $$567\times \frac{1}{4}$$
- step8: Multiply:
  $$\frac{567}{4}$$
Calculate or simplify the expression $$ 2*(\sqrt[3]{64}+\sqrt{25}) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$2\left(\sqrt[3]{64}+\sqrt{25}\right)$$
- step1: Simplify the root:
  $$2\left(4+\sqrt{25}\right)$$
- step2: Simplify the root:
  $$2\left(4+5\right)$$
- step3: Add the numbers:
  $$2\times 9$$
- step4: Multiply the numbers:
  $$18$$
Let's solve each part step by step:

### A. $$ 1 \frac{2}{3}: 2 \frac{3}{3} $$

To simplify $$ 1 \frac{2}{3} : 2 \frac{3}{3} $$:
1. Convert mixed numbers to improper fractions:
   - $$ 1 \frac{2}{3} = \frac{5}{3} $$
   - $$ 2 \frac{3}{3} = 3 $$

2. Now, perform the division:
   $$
   \frac{5}{3} : 3 = \frac{5}{3} \div 3 = \frac{5}{3} \times \frac{1}{3} = \frac{5}{9}
   $$

The result can also be expressed as $$ \frac{7}{3} $$ or $$ 2 \frac{1}{3} $$ or $$ 2.3\dot{3} $$.

### 4.2. $$ 2(\sqrt[3]{64}+\sqrt{25}) $$

1. Calculate $$ \sqrt[3]{64} = 4 $$ and $$ \sqrt{25} = 5 $$.
2. Substitute these values into the expression:
   $$
   2(4 + 5) = 2 \times 9 = 18
   $$

### 4.3. $$ \left(\frac{64}{125}\right)^{x}=\left(\frac{5}{4}\right)^{-x} $$

1. Rewrite the equation:
   $$
   \left(\frac{64}{125}\right)^{x} = \left(\frac{5}{4}\right)^{-x}
   $$

2. Taking logarithms or equating the bases, we find:
   $$
   x = 0
   $$

### 4. $$ 99 x^{2}+(5 x)^{0} $$

1. Since $$ (5x)^{0} = 1 $$:
   $$
   99x^{2} + 1
   $$

### 4. $$ 7 \frac{3^{10} \times 2^{4}}{3^{6} \times 2^{6}} $$

1. Simplify the expression:
   $$
   7 \times \frac{3^{10}}{3^{6}} \times \frac{2^{4}}{2^{6}} = 7 \times 3^{4} \times \frac{1}{2^{2}} = 7 \times \frac{81}{4} = \frac{567}{4} = 141 \frac{3}{4} = 141.75
   $$

### 4 S. Simplify
$$
\frac{16 x 1^{3} \times\left(x^{3} 1\right)^{4}}{\left(2 x^{4} 1^{4}\right)^{3}}
$$

1. Simplifying the expression:
   $$
   = \frac{16 x \times x^{12}}{(2^{3} x^{12})} = \frac{16 x^{13}}{8 x^{12}} = 2x
   $$

### Summary of Results:
- A: $$ \frac{5}{9} $$ or $$ 2 \frac{1}{3} $$ or $$ 2.3\dot{3} $$
- 4.2: $$ 18 $$
- 4.3: $$ x = 0 $$
- 4: $$ 99x^{2} + 1 $$
- 4: $$ 141 \frac{3}{4} $$ or $$ 141.75 $$
- 4 S: $$ 2x $$
A: $$ \frac{5}{9} $$ 4.2: $$ 18 $$ 4.3: $$ x = 0 $$ 4: $$ 99x^{2} + 1 $$ 4: $$ 141 \frac{3}{4} $$ or $$ 141.75 $$ 4 S: $$ 2x $$

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