Solve 2^4div2^-1+(3a)^3-(b+16)*(5-2a)+2^5

$$2 ^ { 4 } \div 2 ^ { - 1 } + ( 3 a ) ^ { 3 } - ( b + 16 ) \cdot ( 5 - 2 a ) + 2 ^ { 5 }$$

Evaluate

$$27a^{3}+2ab+32a-5b-16$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -1 from 4 to get 5.

$$2^{5}+\left(3a\right)^{3}-\left(b+16\right)\left(5-2a\right)+2^{5}$$

Calculate 2 to the power of 5 and get 32.

$$32+\left(3a\right)^{3}-\left(b+16\right)\left(5-2a\right)+2^{5}$$

Expand \left(3a\right)^{3}.

$$32+3^{3}a^{3}-\left(b+16\right)\left(5-2a\right)+2^{5}$$

Calculate 3 to the power of 3 and get 27.

$$32+27a^{3}-\left(b+16\right)\left(5-2a\right)+2^{5}$$

Calculate 2 to the power of 5 and get 32.

$$32+27a^{3}-\left(b+16\right)\left(5-2a\right)+32$$

Use the distributive property to multiply b+16 by 5-2a.

$$32+27a^{3}-\left(5b-2ba+80-32a\right)+32$$

To find the opposite of 5b-2ba+80-32a, find the opposite of each term.

$$32+27a^{3}-5b+2ba-80+32a+32$$

Subtract 80 from 32 to get -48.

$$-48+27a^{3}-5b+2ba+32a+32$$

Add -48 and 32 to get -16.

$$-16+27a^{3}-5b+2ba+32a$$

Expand

$$27a^{3}+2ab+32a-5b-16$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -1 from 4 to get 5.

$$2^{5}+\left(3a\right)^{3}-\left(b+16\right)\left(5-2a\right)+2^{5}$$

Calculate 2 to the power of 5 and get 32.

$$32+\left(3a\right)^{3}-\left(b+16\right)\left(5-2a\right)+2^{5}$$

Expand \left(3a\right)^{3}.

$$32+3^{3}a^{3}-\left(b+16\right)\left(5-2a\right)+2^{5}$$

Calculate 3 to the power of 3 and get 27.

$$32+27a^{3}-\left(b+16\right)\left(5-2a\right)+2^{5}$$

Calculate 2 to the power of 5 and get 32.

$$32+27a^{3}-\left(b+16\right)\left(5-2a\right)+32$$

Use the distributive property to multiply b+16 by 5-2a.

$$32+27a^{3}-\left(5b-2ba+80-32a\right)+32$$

To find the opposite of 5b-2ba+80-32a, find the opposite of each term.

$$32+27a^{3}-5b+2ba-80+32a+32$$

Subtract 80 from 32 to get -48.

$$-48+27a^{3}-5b+2ba+32a+32$$

Add -48 and 32 to get -16.

$$-16+27a^{3}-5b+2ba+32a$$