Ex 13.1 Q2 Exponents and Powers Solution- NCERT Maths Class 7

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Question

Express the following in exponential form:

(i) \(6\times 6\times 6\times 6\)         

(ii) \(t \times t\)

(iii) \(b \times b  \times b  \times b \)

(iv) \(5\times 5\times 7\times 7\times 7\)       

(v) \(2\times 2\times a \times a\) 

(vi)  \(a \times a \times a \times c \times c \times c \times c \times d\)

Text Solution

What is known? 

Base of exponent.

What is unknown?

Power of the base.

Reasoning:

In this question a number is multiplied number of times and we have to express it in exponential form. As we know exponent is the number of times base is multiplied. So, will find the exponent and write it in exponential form.

(i) \(6\times 6\times 6\times 6\)

\(6\) is multiplied \( 4 \) times

Base \(=\) \( 6\) and Exponent \(=\) \(4\)

So, exponential form is \(6^4\)

(ii) \(t \times t\)

\(t\) is multiplied \( 2 \) times

Base \(=\) \( t \) and Exponent \(=\) \( 2 \)

So, exponential form is \(=\) \(t^2\)

(iii) \(b \times b \times b \times b \)

\(b\) is multiplied \(4\) times.

Base \(=\) \(b,\) exponent \(=\)\( 4 \) 

So, exponential form is \(b^4\)

(iv) \(5\times 5\times 7\times 7\times 7\)

\(5\) is multiplied \(2\) times and \(7\) is multiplied 3 times.

Base is \( 5\) and \(7 \) and exponent of \( 5 \) is \( 2\) and \(7\) is \( 3.\) 

So, exponential form is \(=\) \( 5^2\times\)  \(7^3\)

(v) \(2\times 2\times \text{a}\times \text{a}\)

\(2\) is multiplied \(2\) times, a is multiplied \(2\) times.

Base is \(2\) and \( a\) and exponent of \( 2 \) is \( 2\) and \( a\) is \( 2\)

So, exponential form is \(=\) \( 2^2 \times a^2\)  \(\)

(vi) \(a \times a \times a \times c \times c \times c \times c \times d\)

In this,\( a \) is multiplied \(3\) times, \(c\) is multiplied \( 4\) times and \( d \) once.

Base is \(a\)\( c \) and \( d\). Exponent of \(a\) is \(3\), \(c\) is \( 4 \) and \(d \) is \( 1 \) 

So,exponential form is \(a^3\times c^4 \times d\)

  
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