$$ 2 a^{-2} imes 3 a^{3} imes a^{0} $$ c) $$ 3^{-2}+\frac{1}{4^{-2}}+15^{0}-10 $$

Question

$$ 2 a^{-2} 	imes 3 a^{3} 	imes a^{0} $$ c) $$ 3^{-2}+\frac{1}{4^{-2}}+15^{0}-10 $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ 2*a^(-2) * 3*a^3 * a^0 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$2a^{-2}	imes 3a^{3}	imes a^{0}$$
- step1: Evaluate the power:
  $$2a^{-2}	imes 3a^{3}	imes 1$$
- step2: Rewrite the expression:
  $$2a^{-2}	imes 3a^{3}$$
- step3: Multiply the terms:
  $$6a^{-2}	imes a^{3}$$
- step4: Multiply the terms:
  $$6a^{-2+3}$$
- step5: Add the numbers:
  $$6a$$
The simplified form of $$2a^{-2} 	imes 3a^{3} 	imes a^{0}$$ is $$6a$$.

Now, let's calculate the expression $$3^{-2}+\frac{1}{4^{-2}}+15^{0}-10$$.
Calculate the value by following steps:
- step0: Calculate:
  $$3^{-2}+\frac{1}{\left(4^{-2}ight)}+15^{0}-10$$
- step1: Evaluate:
  $$3^{-2}+\frac{1}{4^{-2}}+15^{0}-10$$
- step2: Evaluate the power:
  $$3^{-2}+\frac{1}{4^{-2}}+1-10$$
- step3: Divide the terms:
  $$3^{-2}+16+1-10$$
- step4: Evaluate the power:
  $$\frac{1}{9}+16+1-10$$
- step5: Calculate:
  $$\frac{1}{9}+7$$
- step6: Reduce fractions to a common denominator:
  $$\frac{1}{9}+\frac{7	imes 9}{9}$$
- step7: Transform the expression:
  $$\frac{1+7	imes 9}{9}$$
- step8: Multiply the numbers:
  $$\frac{1+63}{9}$$
- step9: Add the numbers:
  $$\frac{64}{9}$$
The expression $$3^{-2}+\frac{1}{4^{-2}}+15^{0}-10$$ simplifies to $$\frac{64}{9}$$, which is equivalent to $$7\frac{1}{9}$$ or $$7.1$$.
The simplified expression is $$6a$$, and the calculated value is $$\frac{64}{9}$$ or $$7\frac{1}{9}$$.

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