Question

Evaluate the following expressions. Check your answers with a calculator. a. \(15+2 \cdot 5^{3}\) b. \(5 \cdot 2^{4}-3^{3}\) c. \(5^{2} \cdot 2^{3} \div 10-6\) d. \(5^{2} \cdot 2-5 \cdot 2^{3}\)

Short answer

a. \(15 + 2 \cdot 5^{3}\) b. \(5 \cdot 2^{4} - 3^{3}\) c. \(5^{2} \cdot 2^{3} \div 10 - 6\) d. \(5^{2} \cdot 2 - 5 \cdot 2^{3}\) Answer: a. 265 b. 53 c. 14 d. 10

Step-by-step solution

Evaluate the Exponent

First, evaluate the exponent \(5^{3}\): \(5 \cdot 5 \cdot 5 = 125\).

Perform Multiplication

Next, multiply \(2 \cdot 125 = 250\).

Perform Addition

Finally, add \(15 + 250 = 265\). The result of this expression is 265. For expression b. \(5 \cdot 2^{4}-3^{3}\):

Evaluate the Exponents

First, evaluate the exponents \(2^{4}\) and \(3^{3}\): \(2 \cdot 2 \cdot 2 \cdot 2 = 16\) and \(3 \cdot 3 \cdot 3 = 27\).

Perform Multiplication

Next, multiply \(5 \cdot 16 = 80\).

Perform Subtraction

Finally, subtract \(80 - 27 = 53\). The result of this expression is 53. For expression c. \(5^{2} \cdot 2^{3} \div 10-6\):

Evaluate the Exponents

First, evaluate the exponents \(5^{2}\) and \(2^{3}\): \(5 \cdot 5 = 25\) and \(2 \cdot 2 \cdot 2 = 8\).

Perform Multiplication

Next, multiply \(25 \cdot 8 = 200\).

Perform Division

Now, divide \(200 \div 10 = 20\).

Perform Subtraction

Finally, subtract \(20 - 6 = 14\). The result of this expression is 14. For expression d. \(5^{2} \cdot 2-5 \cdot 2^{3}\):

Evaluate the Exponent

First, evaluate the exponents \(5^{2}\) and \(2^{3}\): \(5 \cdot 5 = 25\) and \(2 \cdot 2 \cdot 2 = 8\).

Perform Multiplications

Next, perform the multiplications: \(25 \cdot 2 = 50\) and \(5 \cdot 8 = 40\).

Perform Subtraction

Finally, subtract \(50 - 40 = 10\). The result of this expression is 10. So, the evaluated expressions are: a. \(15 + 2 \cdot 5^3 = 265\) b. \(5 \cdot 2^4 - 3^3 = 53\) c. \(5^2 \cdot 2^3 \div 10 - 6 = 14\) d. \(5^2 \cdot 2 - 5 \cdot 2^3 = 10\)