Decimal Fractions MCQs with Answers & Explanations (Page 4)

Rewrite y^5 as the product of the largest perfect square (y^4) and y. The square root of y^4 is y^2, bringing it outside the radical to get y^2*sqrt(y).

Adding the first two numbers produces exactly 20.0000. Subtracting 8.9995 from 20.0000 gives an end result of 11.0005.

To evaluate the cube root of 512, we identify the number that gives 512 when cubed. Since 8 * 8 * 8 = 512, the answer is 8.

To multiply expressions with identical bases, you must add the exponents while keeping the base unchanged. Adding 2 and 5 gives an exponent of 7, resulting in 5^7.

To remove the radical from the denominator, multiply both numerator and denominator by sqrt(2). This results in (1 * sqrt(2)) / (sqrt(2) * sqrt(2)), which simplifies to sqrt(2) / 2.

Any non-zero variable or number raised to the zero power simplifies to exactly 1. Thus, as long as x is not zero, x^0 = 1.

Applying the power rule, we multiply the exponent inside the parentheses by the exponent outside. The product of 5 and 2 is 10, so the expression simplifies to y^10.

Because the entire expression (2xy) is enclosed in parentheses and raised to the power of zero, the zero exponent rule applies to the whole term, resulting in 1.

To multiply a fraction by a whole number, the whole number is treated as a numerator over 1 (i.e., 4 = $\frac{4}{1}$). You then multiply the numerators together ($3 \times 4 = 12$) and the denominators together ($5 \times 1 = 5$). This results in the fraction $\frac{12}{5}$. The other options represent common errors, such as multiplying the denominator by the whole number or adding instead of multiplying.

When multiplying two fractions, the numerators are multiplied by each other, and the denominators are multiplied by each other. For this problem, you multiply the numerators $2 \times 4$ to get 8. Then, you multiply the denominators $7 \times 5$ to get 35. The resulting product is $\frac{8}{35}$. This fraction is already in its simplest form as 8 and 35 share no common factors other than 1.

Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. Therefore, the expression is rewritten as $6 \times \frac{3}{2}$. Treating the whole number 6 as $\frac{6}{1}$, we multiply the numerators ($6 \times 3 = 18$) and the denominators ($1 \times 2 = 2$). The resulting fraction is $\frac{18}{2}$, which simplifies to the whole number 9.

The cube root of 1000 requires finding the base that creates 1000 when multiplied by itself three times. 10 * 10 * 10 equals 1000, so the answer is 10.

First, add the exponents: 3 + (-5) = -2, giving x^-2. Then, convert the negative exponent to a positive one by rewriting it as 1/x^2.

A negative exponent flips the position of the term in a fraction. Changing y^-4 to a positive exponent moves it to the denominator, becoming 1/y^4.

When a term with an exponent is raised to an additional power, the exponents are multiplied. Multiplying 3 by 5 yields 15, making the simplified term z^15.

The number 54 can be divided by the perfect cube 27 (27 * 2 = 54). Evaluating the cube root of 27 gives 3, so the expression simplifies to 3*cbrt(2).

When multiplying powers of 10, the base remains 10 and the exponents are summed. The sum of 3 and 4 is 7, making the final expression 10^7.

By applying the fundamental rule of exponents for multiplication, we add the exponents 2 and 3. The base remains 4, which gives us 4^5.

Raising to the power of 1/3 means finding the cube root. The cube root of 125 is 5, since 5 cubed (5 * 5 * 5) is equal to 125.

For negative numbers, a larger absolute magnitude equates to a smaller value. Evaluating them: -7/10 = -0.700, -2/3 ≈ -0.667, -5/8 = -0.625. Ordering these from smallest to largest yields -7/10, -2/3, -5/8.