Question

Simplify with explanation ​

Answer 1

Answer:

may this helps you

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Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To Simplify:

• $\dfrac{3^{-4} * 2^6 * (-7)^4}{4^5 * 49^2 * 9^{-2}}$

Solution:

$:\longrightarrow \dfrac{3^{-4} * 2^6 * (-7)^4}{4^5 * 49^2 * 9^{-2}} \\\\:\implies \dfrac{3^{-4} * 2^6 * (-7)^4}{2^{2^5} * (-7)^{2^2} * 3^{2^{-2}}} \\\\:\implies \dfrac{3^{-4} * 2^6 * (-7)^4}{2^{10} * (-7)^{4} * 3^{-4}} \\\\:\implies 2^{6-10} * 3^{-4-(-4)} * (-7)^{4-4} \\\\:\implies 2^{-4} * 3^{-4+4} * 7^{0} \\\\:\implies 2^{-4} * 3^0 * 1 \\\\\bf{:\implies 2^{-4} \:\:\: OR \:\:\: \dfrac{1}{2^4} \:\:\:OR\:\:\: \dfrac{1}{16}}$

Formula used:

• a^m ÷ a^n = a^{m-n}
• (a^m)^n = a^mn
• a^0 = 1

Learn More:

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$