Ex 13.1 Q7 Exponents and Powers Solution- NCERT Maths Class 7

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Question

Simplify:

(i) \({{(-4)}^{3}}\)

(ii) \((-3)\times {{(-2)}^{3}}\)

(iii) \({{(-3)}^{2}}\times {{(-5)}^{2}}\)

(iv)  \({{(-2)}^{3}}\times {{(-10)}^{3}}\)

Text Solution

What is unknown?

Base and Exponent

Reasoning:

In this question we will multiply the base and the number of times it’s exponent to simplify the given statement.  

Steps:

(i) \({{(-4)}^{3}}\)

\[\begin{align} &\!=\!-4\times\! -4\!\times\! -4\!\\&=\!-\!64 \end{align}\]

(ii) \((-3)\times {{(-2)}^{3}}\)

\[\begin{align}&=\!-3x\left( -2\!\times\!\!\!-2\times\!\!-2 \right)\\&=-3\!\times\!\!-8\\&=24\end{align}\]

(iii) \({{(-3)}^{2}}\times {{(-5)}^{2}}\)

\[\begin{align}&\!=\!-3x\!-\!3x(\!-5x\!-5)\\&=9\times 25\\&=225 \end{align}\]

(iv)  \({{(-2)}^{3}}\times {{(-10)}^{3}}\)

\[\begin{align}&\!=\!-\!\!2x\!-\!\!2x\!-\!\!2x(\!-\!\!10x\!-\!\!10x\!-\!\!10)\\&=-8x-1000\\&=8000 \end{align}\]

  
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