simplify simplify using laws of exponents:-
a) 25⁴ ÷ 5⁶
b) (7¹⁵×7⁵)÷7⁹
with explanation
Answers
Answer:
Answer:
\begin{gathered}a) \: \: \: \frac{ {25}^{4} }{ {5}^{6} } \\ = \frac{ { {(5}^{2}) }^{4} }{ {5}^{6} } \\ = \frac{ {(5)}^{2 \times 4} }{ {5}^{6} } \\ = \frac{ {5}^{8} }{ {5}^{6} } \\ = {(5)}^{8 - 6} \\ = {5}^{2} \\ \large{ \boxed{= \underline{ \underline{25}}}} \\ \\ b) \: \: \: \frac{ {7}^{15} \times {7}^{5} }{ {7}^{9} } \\ = \frac{ {(7)}^{15 + 5} }{ {7}^{9} } \\ = \frac{ {7}^{20} }{ {7}^{9} } \\ = {(7)}^{20 - 9} \\ \large{ \boxed{= \underline{ \underline{ {7}^{13} }}}} \\ \\ \large{ \underline{Note} :} \\ * \: \: \: {( {a}^{m}) }^{n} = {(a)}^{m \times n} = {(a)}^{mn} \\ * \: \: \: {a}^{m} \times {a}^{n} = {(a)}^{m + n} \\ * \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {(a)}^{m - n} \end{gathered}
a)
5
6
25
4
=
5
6
(5
2
)
4
=
5
6
(5)
2×4
=
5
6
5
8
=(5)
8−6
=5
2
=
25
b)
7
9
7
15
×7
5
=
7
9
(7)
15+5
=
7
9
7
20
=(7)
20−9
=
7
13
Note
:
∗(a
m
)
n
=(a)
m×n
=(a)
mn
∗a
m
×a
n
=(a)
m+n
∗
a
n
a
m
=(a)
m−n