Question

please simplify (2)question step by step its very urgent​

Answer 1

(i) $5^{\frac{2}{3}}\times 5^{\frac{4}{3}}$

Here we need to apply this law of exponent ⇒ $a^m\times a^n=a^{m+n}$

$5^{\frac{2}{3}}\times 5^{\frac{4}{3}}$

$5^{\frac{2}{3}+\frac{4}{3}$

$5^{\frac{6}{3}$

$5^2$

$25$

∴ $5^{\frac{2}{3}}\times 5^{\frac{4}{3}}=25$

(ii) $[(4)^\frac{1}{2}]^6$

Here we need to apply this law of exponent ⇒ $(a^m)^n=a^{m\times n}$

$[(4)^\frac{1}{2}]^6$

$[4]^{\frac{1}{2} \times 6}$

$[4]^3$

$64$

∴ $[(4)^\frac{1}{2}]^6=64$

Additional Information :)

What are exponents?

Something that says how many times to use the number in a multiplication is known as an exponent.

What are the laws of exponents?

There are many laws of exponents. They are -

• $a^m\times a^n=a^{m+n}$
• $a^m\div a^n=a^{m-n}$
• $a^m\times b^m=(ab)^m$
• $a^m \div b^m = (\frac{a}{b})^m$
• $(a^m)^n=a^{m\times n}$
• $\frac{a^m}{b^m}=(\frac{a}{b})^m$
• $a^0=1$
• $a^{-m}=\frac{1}{a^m}$