Powers and Roots: Solving the equation

Remember that according to the order of operations, exponents come before multiplication and division, which come before addition and subtraction (and parentheses always before everything),

So first calculate the values of the terms in the power and then subtract between the results:

$3^2-3^3 =9-27=-18$Therefore, the correct answer is option A.

Remember that according to the order of operations, exponents precede multiplication and division, which precede addition and subtraction (and parentheses always precede everything).

So first calculate the values of the terms in the power and then subtract between the results:

$3^2+3^3 =9+27=36$Therefore, the correct answer is option B.

Remember that according to the order of arithmetic operations, exponents precede multiplication and division, which precede addition and subtraction (and parentheses always precede everything).

So first calculate the values of the terms with exponents and then subtract the results:

$5^2\cdot4+3^3 =25\cdot4+27=100+27=127$Therefore, the correct answer is option B.

Let's solve the problem step by step using the Zero Exponent Rule, which states that any non-zero number raised to the power of 0 is equal to 1.

• Consider the expression: $100^0$.
• According to the Zero Exponent Rule, if we have any non-zero number, say $a$, then $a^0 = 1$.
• Here, $a = 100$ which is clearly a non-zero number, so following the rule, we find that:
• $100^0 = 1$.

Therefore, the expression $100^0$ is equivalent to 1.

We simplify each term according to the order from left to right:

$\sqrt{4}=2$

$4^2=4\times4=16$

$5^2=5\times5=25$$$

$\sqrt{1}=1$

Now we rearrange the exercise accordingly:

$2\times16-25\times1$

Since there are two multiplication operations in the exercise, according to the order of operations we start with them and then subtract.

We put the two multiplication exercises in parentheses to avoid confusion during the solution, and solve from left to right:

$(2\times16)-(25\times1)=32-25=7$