QuestionWhat is the value of $\frac{a^{3}-b^{3}}{5}$ for $a=2$ and $b=-3$ ? Options: $-3 \frac{4}{5}$ , $-\frac{3}{5}$ , 3, 7.

Studdy Solution

STEP 1

Assumptions1. The value of $a$ is. The value of $b$ is -33. We need to substitute these values into the expression $\frac{a^{3}-b^{3}}{5}$

STEP 2

Substitute the given values of $a$ and $b$ into the expression.
$\frac{a^{}-b^{}}{5} = \frac{2^{}-(-)^{}}{5}$

STEP 3

Calculate the values of $2^{3}$ and $(-3)^{3}$ .
$2^{3} =8$ $(-3)^{3} = -27$

STEP 4

Substitute these calculated values back into the expression.
$\frac{8 - (-27)}{}$

STEP 5

implify the expression inside the numerator. Remember that subtracting a negative number is equivalent to adding a positive number.
$\frac{8 +27}{5}$

STEP 6

Calculate the value inside the numerator.
$8 +27 =35$

STEP 7

Substitute this value back into the expression.
$\frac{35}{5}$

STEP 8

Finally, calculate the value of the expression.
$\frac{35}{5} =7$ So, the value of the expression when $a=2$ and $b=-3$ is7.

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QuestionWhat is the value of $\frac{a^{3}-b^{3}}{5}$ for $a=2$ and $b=-3$ ? Options: $-3 \frac{4}{5}$ , $-\frac{3}{5}$ , 3, 7.

Studdy Solution

STEP 1

Assumptions1. The value of $a$ is. The value of $b$ is -33. We need to substitute these values into the expression $\frac{a^{3}-b^{3}}{5}$

STEP 2

Substitute the given values of $a$ and $b$ into the expression.
$\frac{a^{}-b^{}}{5} = \frac{2^{}-(-)^{}}{5}$

STEP 3

Calculate the values of $2^{3}$ and $(-3)^{3}$ .
$2^{3} =8$ $(-3)^{3} = -27$

STEP 4

Substitute these calculated values back into the expression.
$\frac{8 - (-27)}{}$

STEP 5

implify the expression inside the numerator. Remember that subtracting a negative number is equivalent to adding a positive number.
$\frac{8 +27}{5}$

STEP 6

Calculate the value inside the numerator.
$8 +27 =35$

STEP 7

Substitute this value back into the expression.
$\frac{35}{5}$

STEP 8

Finally, calculate the value of the expression.
$\frac{35}{5} =7$ So, the value of the expression when $a=2$ and $b=-3$ is7.

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QuestionWhat is the value of a3−b35\frac{a^{3}-b^{3}}{5}5a3−b3​ for a=2a=2a=2 and b=−3b=-3b=−3? Options: −345-3 \frac{4}{5}−354​, −35-\frac{3}{5}−53​, 3, 7.

Studdy Solution

STEP 1

Assumptions1. The value of aaa is. The value of bbb is -33. We need to substitute these values into the expression a3−b35\frac{a^{3}-b^{3}}{5}5a3−b3​

STEP 2

Substitute the given values of aaa and bbb into the expression.a−b5=2−(−)5\frac{a^{}-b^{}}{5} = \frac{2^{}-(-)^{}}{5}5a−b​=52−(−)​

STEP 3

Calculate the values of 232^{3}23 and (−3)3(-3)^{3}(−3)3.23=82^{3} =823=8(−3)3=−27(-3)^{3} = -27(−3)3=−27

STEP 4

Substitute these calculated values back into the expression.8−(−27)\frac{8 - (-27)}{}8−(−27)​

STEP 5

implify the expression inside the numerator. Remember that subtracting a negative number is equivalent to adding a positive number.8+275\frac{8 +27}{5}58+27​

STEP 6

Calculate the value inside the numerator.8+27=358 +27 =358+27=35

STEP 7

Substitute this value back into the expression.355\frac{35}{5}535​

STEP 8

Finally, calculate the value of the expression.355=7\frac{35}{5} =7535​=7So, the value of the expression when a=2a=2a=2 and b=−3b=-3b=−3 is7.

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QuestionWhat is the value of $\frac{a^{3}-b^{3}}{5}$ for $a=2$ and $b=-3$ ? Options: $-3 \frac{4}{5}$ , $-\frac{3}{5}$ , 3, 7.

Assumptions1. The value of $a$ is. The value of $b$ is -33. We need to substitute these values into the expression $\frac{a^{3}-b^{3}}{5}$

Substitute the given values of $a$ and $b$ into the expression.
$\frac{a^{}-b^{}}{5} = \frac{2^{}-(-)^{}}{5}$

Calculate the values of $2^{3}$ and $(-3)^{3}$ .
$2^{3} =8$ $(-3)^{3} = -27$

Substitute these calculated values back into the expression.
$\frac{8 - (-27)}{}$

implify the expression inside the numerator. Remember that subtracting a negative number is equivalent to adding a positive number.
$\frac{8 +27}{5}$

Calculate the value inside the numerator.
$8 +27 =35$

Substitute this value back into the expression.
$\frac{35}{5}$

Finally, calculate the value of the expression.
$\frac{35}{5} =7$ So, the value of the expression when $a=2$ and $b=-3$ is7.