hey, can anyone explain negative integral exponents to me with examples? will really appreciate your help!
Answers
Answer:
Definition for negative exponents
We define a negative power as the multiplicative inverse of the base raised to the positive opposite of the power:
x^{-n}=\dfrac{1}{x^n}x
−n
=
x
n
1
x, start superscript, minus, n, end superscript, equals, start fraction, 1, divided by, x, start superscript, n, end superscript, end fraction
Want to learn more about this definition? Check out this video.
Examples
3^{-5}=\dfrac{1}{3^5}3
−5
=
3
5
1
3, start superscript, minus, 5, end superscript, equals, start fraction, 1, divided by, 3, start superscript, 5, end superscript, end fraction
\dfrac{1}{2^8}=2^{-8}
2
8
1
=2
−8
start fraction, 1, divided by, 2, start superscript, 8, end superscript, end fraction, equals, 2, start superscript, minus, 8, end superscript
y^{-2}=\dfrac{1}{y^{2}}y
−2
=
y
2
1
y, start superscript, minus, 2, end superscript, equals, start fraction, 1, divided by, y, squared, end fraction
\left(\dfrac{8}{6}\right)^{-3}=\left(\dfrac{6}{8}\right)^{3}(
6
8
)
−3
=(
8
6
)
3
Negative Integral Exponent of a Rational Number
Let a/b be any rational number and n be a positive integer. Then, we define, (a/b)−n = (b/a)ⁿ For example: (i) (3/4)−5. = (4/3)⁵