For questions 14-15, find the simplified form of each expression.
(3/2b^4)^3
(3/5y^4)^-2
(3/2b^4)^3
= (27/8)b^12
(3/5y^4)^-2
= 1/(3/5y^4)^2
= 1/( (9/25)y^8
= 25/(9y^8)
or
(25/9)y^-8
Reiny, Steve!! I need help!
Can you help me with some graph ones?
[ ( 3 / 2 ) b ^ 4 ] ^ 3 =
[ ( 3 ^ 3 ) / ( 2 ^ 3 ) ] * ( b ^ 4 ) ^ 3 =
( 27 / 8 ) * b ^ ( 4 * 3 ) =
( 27 / 8 ) * b ^ 12 =
27 b ^ 12 / 8
( 3 / 5 y ^ 4 )^ ( - 2 ) =
[ ( 3 ^ ( - 2 ) ] / [ ( 5 ^ ( - 2 ) ] * [ y ^ 4 ^ ( - 2 ) ] =
( 1 / 3 ^ 2 ) / ( 1 / 5 ^ 2 ) * y ^ [ 4 * ( - 2 ) ] =
( 1 / 9 ) / ( 1 / 25 ) * ( y ^ - 8 ) =
[ ( 1 * 25 ) / ( 1 * 9 ) ] * 1 / y ^ 8 =
( 25 / 9 ) * 1 / y ^ 8 =
25 / 9 y ^ 8
(3/2b^4)^3 simplified is 27/8b^12 because math is just a fancy way of turning numbers into fractions and confusing everyone.
(3/5y^4)^-2 simplified is 25/9y^8 because negative exponents are just a way for numbers to play hide and seek.
To find the simplified form of each expression, we need to apply the exponent rule.
For the first expression, (3/2b^4)^3:
Step 1: Simplify the base by raising it to the power of 3.
(3/2)^3 * (b^4)^3
Step 2: Simplify each term.
(27/8) * b^(4 * 3)
Step 3: Simplify the exponents.
27/8 * b^12
So, the simplified form of (3/2b^4)^3 is 27/8 * b^12.
For the second expression, (3/5y^4)^-2:
Step 1: Apply the reciprocal rule by flipping the base with the negative exponent.
(5y^4/3)^2
Step 2: Square each term.
(5^2 * y^(4 * 2)) / (3^2)
Step 3: Simplify the exponents and evaluate the values.
(25 * y^8) / 9
So, the simplified form of (3/5y^4)^-2 is (25y^8)/9.
Fractions
1-(2/3+1/5)=