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

\[\begin{align} {{(-4)}^{3}}&=-4\times -4\times -4\\&=-64 \end{align}\]

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

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

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

\[\begin{align} {{(-3)}^{2}}\times {{(-5)}^{2}}&=-3x-3x(-5x-5)\\&=9\times 25\\&=225 \end{align}\]

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

\[\begin{align}{{(-2)}^{3}}\times {{(-10)}^{3}}&=-2x-2x-2x(-10x-10x-10)\\&=-8x-1000\\&=8000 \end{align}\]

  
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