To evaluate [2/3]² ÷ [4/5]³ × [3/5]², we start by squaring or cubing the fractions in brackets. We then convert the division operation to multiplication by taking the reciprocal of the divisor. Multiplying straight across yields the final result of 5/16.
To evaluate the expression [2/3]² ÷ [4/5]³ × [3/5]², start by performing the operations in the square brackets. Taking the square of 2/3 and 3/5, and the cube of 4/5 we get:
(2/3)²=4/9
(4/5)³=64/125
(3/5)²=9/25
Plug these values back into the expression: [4/9] ÷ [64/125] × [9/25]
Before you perform the operations, it's easier to convert the division operation to multiplication by taking the reciprocal of the divisor. The expression becomes:
4/9 * 125/64 * 9/25
Now, multiply straight across, we get: 4500/14400 = 5/16
So, [2/3]² ÷ [4/5]³ × [3/5]² evaluates to 5/16.
Learn more about Fraction Operations