Question

find m when (5^m÷5^-3)×5²=5³ plz don't give irrelevant answers if you are giving give correct answers​

Answer 1

Given:

• $\sf {(5^{m} \div 5^{-3}) \times 5^{2} = 5^{3}}$

To find:

• Value of m.

Solution:

$\sf {(5^{m} \div 5^{-3}) \times 5^{2} = 5^{3}}$

$\bigstar {\sf{ \pink{Using \: law \: of \: indices \: {a}^{m} \div {a}^{n} = {a}^{m - n} } }}$

$\sf {5^{m-(-3)} \times 5^{2} = 5^{3}}$

$\sf {5^{m+3} \times 5^{2} = 5^{3}}$

$\bigstar {\sf{ \orange{Using \: law \: of \: indices \: {a}^{m} \times {a}^{n} = {a}^{m + n} } }}$

$\sf {5^{m+3+2} = 5^{3}}$

$\sf {5^{m+5} = 5^{3}}$

$\bigstar {\sf {\purple {On\ equating\ the\ powers\ of\ 5}}}$

m+5 = 3

m = 3-5

$\boxed {\bf {\red {m = -2}}}$

Verification:

Substitute the value of m as (-2),

$\sf {(5^{m} \div 5^{-3}) \times 5^{2} = 5^{3}}$

$\sf {(5^{-2} \div 5^{-3}) \times 5^{2} = 5^{3}}$

$\sf {5^{-2-(-3)} \times 5^{2} = 5^{3}}$

$\sf {5^{-2+3} \times 5^{2} = 5^{3}}$

$\sf {5^{1} \times 5^{2} = 5^{3}}$

$\sf {5^{1+2} = 5^{3}}$

$\sf {5^{3} = 5^{3}}$

LHS = RHS

LHS = RHSHence Verified!

Value of m:

Value of m is (-2).