Question

Argghhh no ones answering my questions. could SOMEONE please answer theses questions

Answer 1

Without a calculator


$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}} \\\\\\ ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------\\\\ 3^4\implies 3\cdot 3\cdot 3\cdot 3\implies \boxed{81} \\\\\\ 27=3^3\qquad \qquad \sqrt[3]{27}\implies \sqrt[3]{3^3}\implies 3^{\frac{3}{3}}\implies 3^1\implies \boxed{3}$

$\bf 2^5\implies 2\cdot 2\cdot 2\cdot 2\cdot 2\implies \boxed{32} \\\\\\ \left( \cfrac{2}{3} \right)^2\implies \cfrac{2^2}{3^2}\implies \boxed{\cfrac{4}{9}} \\\\\\ 64=4^3\qquad \qquad \sqrt[3]{64}\implies \sqrt[3]{4^3}\implies 4^{\frac{3}{3}}\implies 4^1\implies \boxed{4} \\\\\\ (-2)^3\implies -2\cdot -2\cdot -2\implies \boxed{-8} \\\\\\ (0.8)^2\implies 0.8\cdot 0.8\implies \boxed{0.64}$

$\bf 12100=110^2\qquad \qquad \sqrt{12100}\implies \sqrt[2]{110^2}\implies 110^{\frac{2}{2}}\\\\\\ 110^1\implies \boxed{110}$



simplifying into



$\bf 7^2\times 7^3\implies 7^{2+3}\implies 7^5\implies \boxed{16807} \\\\\\ 8^2\div 8^5\implies 8^{2-5}\implies 8^{-3}\implies \cfrac{1}{8^3}\implies \boxed{\cfrac{1}{512}} \\\\\\ 9^5\times 9^{-6}\implies 9^{5+(-6)}\implies 9^{-1}\implies \boxed{\cfrac{1}{9}} \\\\\\ 2^{-4}\div 2^{-9}\implies 2^{-4-(-9)}\implies 2^{-4+9}\implies 2^5\implies \boxed{32} \\\\\\ \stackrel{\textit{anything raised at 0, is 1, only exception being 0 itself}}{6^0\implies \boxed{1}}$

Answer 2

Answer:

1. 16807

2: 1/512

3: 1/9

4: 32

5: 1

Step-by-step explanation: