Simplify the expression using the properties of exponents. Expand any numerical portion of your answer and only include positive exponents.
(4x^3y^−1)^−3/(5x^−2y)^−3
To simplify the given expression using the properties of exponents, we will employ the rules of negative exponents, reciprocal exponents, and the power of a power rule.
First, let's apply the reciprocal exponent rule to the numerator and denominator separately:
(4x^3y^−1)^−3 can be rewritten as 1/(4x^3y^−1)^3
Similarly, (5x^−2y)^−3 can be rewritten as 1/(5x^−2y)^3
Next, let's apply the power of a power rule to both the numerator and denominator:
(4x^3y^−1)^3 simplifies to 64x^9y^−3 (since 4^3 = 64, (x^3)^3 = x^9, and (y^−1)^3 = y^−3)
Similarly, (5x^−2y)^3 simplifies to 125x^−6y^3 (since 5^3 = 125, (x^−2)^3 = x^−6, and y^3 remains the same)
Now, let's substitute the simplified values back into our expression:
1/(4x^3y^−1)^3 becomes 1/(64x^9y^−3)
1/(5x^−2y)^3 becomes 1/(125x^−6y^3)
Finally, let's multiply the numerator and denominator by the reciprocal of the denominator:
1/(64x^9y^−3) * (125x^−6y^3/1) becomes (125x^−6y^3)/(64x^9y^−3)
To simplify this expression further, we can rearrange the terms and combine like terms:
(125/64)(x^−6/x^9)(y^3/y^−3)
Applying the rules of exponents, x^−6/x^9 simplifies to x^(−6−9) = x^−15,
and y^3/y^−3 simplifies to y^(3−−3) = y^6.
Therefore, the simplified expression is:
(125/64)x^−15y^6
What episodes were Steve Urkel most popular
Steve Urkel, a character played by Jaleel White, gained significant popularity for his portrayal on the television show "Family Matters." While Steve Urkel was a recurring character throughout the show's entire run, his popularity was especially prominent during the mid to late 1990s.
It is important to note that Steve Urkel became so popular that he even became the show's central character, with storylines often revolving around his wacky antics and humorous interactions with the Winslow family.
However, rather than specific episodes, it was Steve Urkel as a character who gained popularity over the course of the show's nine-season run from 1989 to 1998.