Simplify 2 X 2 raise to the power 5 X 3raise to the power 4
9 X 4 raise to the power 2 using the laws of exponents.
Answers
Answer :-
625
To solve :-
\begin{gathered}\sf (-3)^4 \times (\frac{5}{3})^4 \\\end{gathered}
(−3)
4
×(
3
5
)
4
Solution :-
We know that, if a negative number is raised to an even power, then the product is positive.
So, \sf -3^4 = 81−3
4
=81
Now,
\begin{gathered}\sf -3^4 \times (\frac{5}{3})^4 \\\\\implies 81 \times \frac{5^4}{3^4}\\\\(since, (\frac{a}{b})^m = \frac{a^m}{b^m })\\\\\implies 81 \times \frac{625}{81}\\\\\implies 625\end{gathered}
−3
4
×(
3
5
)
4
⟹81×
3
4
5
4
(since,(
b
a
)
m
=
b
m
a
m
)
⟹81×
81
625
⟹625
Hence, the answer is 625.
Other Laws Of Exponents :
\begin{gathered}\sf a^m \times a^n = a^{m + n} \\ \\ a^m \div a^n = a^{m - n} \\ \\ a^0 = 1 \\ \\ a^m \times b^m = (ab)^m \end{gathered}
a
m
×a
n
=a
m+n
a
m
÷a
n
=a
m−n
a
0
=1
a
m
×b
m
=(ab)
m