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Powers with Negative Exponents

Express the f...

Question

Express the following with a single exponent. (3 marks)
i. ${(3^{4})}^{- 2}$
ii. ${({(\frac{1}{7})}^{- 3})}^{4}$
iii. ${({(\frac{2}{5})}^{- 3})}^{2}$

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Solution

i. ${(3^{4})}^{- 2} = 3^{4 \times (- 2)} = 3^{- 8}$

(1 mark)

ii. ${({(\frac{1}{7})}^{- 3})}^{4} = {(\frac{1}{7})}^{- 3 \times 4} = {(\frac{1}{7})}^{- 12}$

(1 mark)

iii. ${({(\frac{2}{5})}^{- 3})}^{2} = {(\frac{2}{5})}^{- 3 \times 2} = {(\frac{2}{5})}^{- 6}$

(1 mark)

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Similar questions

Q. Express each of the following rational numbers with a positive exponent:
(i)

{(\frac{3}{4})}^{- 2}

{(\frac{5}{4})}^{- 3}

4^{3} \times 4^{- 9}

{\{{(\frac{4}{3})}^{- 3}\}}^{- 4}

{\{{(\frac{3}{2})}^{4}\}}^{- 2}

Q. Simplify

(i)

{[{(\frac{15}{12})}^{3}]}^{4}

{(3^{4})}^{- 2}

{({(\frac{1}{7})}^{- 3})}^{4}

{({(\frac{2}{5})}^{- 2})}^{- 3}

{(6^{5})}^{4}

{[{(\frac{6}{7})}^{5}]}^{2}

{[{(\frac{2}{3})}^{- 4}]}^{5}

{[{(\frac{5}{8})}^{3}]}^{- 2}

{[{(\frac{3}{4})}^{6}]}^{1}

{[{(\frac{2}{5})}^{- 3}]}^{2}

Q. Verify the following:
(i)

(\frac{3}{4} + \frac{- 2}{5}) + \frac{- 7}{10} = \frac{3}{4} + (\frac{- 2}{5} + \frac{- 7}{10})

(\frac{- 7}{11} + \frac{2}{- 5}) + \frac{- 13}{22} = \frac{- 7}{11} + (\frac{2}{- 5} + \frac{- 13}{22})

- 1 + (\frac{- 2}{3} + \frac{- 3}{4}) = (- 1 + \frac{- 2}{3}) + \frac{- 3}{4}

Determine:
(i) $\frac{3}{4}$ of $16$ cups

(ii) $\frac{3}{4}$ of $28$ rackets

(iii) $\frac{3}{4}$ of $32$ books

Q. Simplify and express the result in power notation with positive exponent.
(i)

(- 4)^{5} \div (- 4)^{8}

{(\frac{1}{2^{3}})}^{2}

(- 3)^{4} \times {(\frac{5}{3})}^{4}

(3^{- 7} \div 3^{- 10}) \times 3^{- 5}

2^{- 3} \times (- 7)^{- 3}

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