Question
Express the following in single exponential form:
$\left(-5^5\right) \times(-5)$
$\left(-5^5\right) \times(-5)$
✓
Answer
$\text { We have, }\left(5^5\right) \times(-5)$
$=(5)^{5+1} \times(-5)^6$
$=(-1 \times 5)^6\left[\because a^m \times a^n=a^{m+n}\right]$
$=(-1)^6 \times(5)^6\left[\because(a \times b)^m=a^m \times b^m\right]$
$=1 \times 5^6\left[\because(-1)^n=1, \text { if } n \text { is even }\right]$
$=5^6$
$=(5)^{5+1} \times(-5)^6$
$=(-1 \times 5)^6\left[\because a^m \times a^n=a^{m+n}\right]$
$=(-1)^6 \times(5)^6\left[\because(a \times b)^m=a^m \times b^m\right]$
$=1 \times 5^6\left[\because(-1)^n=1, \text { if } n \text { is even }\right]$
$=5^6$
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