Simplify [9^ 2^4 9^5 ]÷9^8 - Vidyadip

Question

Simplify $\left[9^{2^4} \times 9^5\right]÷9^8$

✓

Answer

Given, $\left[9^{2^4} \times 9^5\right] \div 9^8$
Now, $\left[\left(9^2\right)^4 \times 9^5\right]÷9^8$
$=\left[9^8 \times 9^5\right]÷9^8 \quad\left[\because\left(x^a\right)^b=x^{a^b}\right]$
$=\left(9^{8+5}\right) \div 9^8 \quad\left[\because x^a \times x^b=x^{a+b}\right]$
$=9^{13} \div 9^8=9^{13-8}=9^5 \quad\left[\because x^a÷x^b=x^{a+b}\right]$
$=9 \times 9 \times 9 \times 9 \times 9=59049$
Hence, $\left[9^{2^4} \times 9^5\right]÷9^8$ is 59049.

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