Simplify the following:

$3^2 \times 3^4 \times 3^8$

$(5^2)^3 \div 5^3$

Given :

The given expressions are $3^2 \times 3^4 \times 3^8$ and $(5^2)^3 \div 5^3$.

To do :

We have to simplify the given expressions.

Solution :

$3^2 \times 3^4 \times 3^8$ 

We know that,

$a^m \times a^n = a^{m+n}$

$3^2 \times 3^4 \times 3^8 = 3^{2+4+8} = 3^14$

Therefore, the simplified form of $3^2 \times 3^4 \times 3^8$  is $3^14$.

$(5^2)^3 \div 5^3$

We know that,

$(a^m)^n = a^{m \times n}, a^m \div a^n = a{m-n}$

$(5^2)^3 \div 5^3 = 5^{2\times 3} \div 5^3 = 5^6 \div 5^3 = 5^{6-3} = 5^3$

Therefore, the simplified form of $(5^2)^3 \div 5^3$ is $5^3$.

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Updated on: 10-Oct-2022

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