Test Index

BECE Mathematics 2023 Paper

© africaexams.com

Question : 38

Total: 40

Simplify:

\;\frac{5^7 \times 5^{-4}}{5^3}

0
1
5
25

Solution:

Law of multiplication of indices

a^m \times a^n=a^{m+m}

Law of division of indices

\;\;\frac{a^m}{a^n}=a^{m-n}

\;a^0=1

\;\;\frac{5^7 \times 5^{-4}}{5^3}=\;\frac{5^{7+-4}}{5^3}

\;\;\frac{5^7 \times 5^{-4}}{5^3}=\;\frac{5^{7-4}}{5^3}

\;\;\frac{5^7 \times 5^{-4}}{5^3}=\;\frac{5^3}{5^3}=1

Note:

5^3

divides

5^3

once.

Alternatively, the law of division could be applied.

\;\;\frac{a^m}{a^n}=a^{m-n}

\;\;\frac{5^3}{5^3}=5^{3-3}

\;\;\frac{5^3}{5^3}=5^0=1

\;5^0=1 (a^0=1)

© africaexams.com

Go to Question:

Prev Question

Next Question