Practice HAT questions with answers and explanations.
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An exponent of 1/2 represents a square root.
Thus, 16^(1/2) = √16 = 4.
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Since 32 = 2⁵, the exponents must be equal.
Therefore, x = 5.
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The logarithm asks what power of 10 gives 1,000.
Since 10³ = 1,000, the answer is 3.
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The logarithmic equation means x = 2⁶.
Thus, x = 64.
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The common difference is 4.
Adding 4 to 19 gives 23.
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Multiply both sides by 4.
Thus, x = 7 × 4 = 28.
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The nth term is a + (n - 1)d.
Thus, 3 + 9 × 4 = 39.
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Adding the equations gives 2x = 14, so x = 7.
Substituting into x + y = 10 gives y = 3.
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Each term is multiplied by 2.
Thus, 24 × 2 = 48.
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Substitute x = 2 to obtain 4 + 3y = 13.
Then 3y = 9, so y = 3.
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The common ratio is 3, so a₆ = 2 × 3⁵.
This equals 2 × 243 = 486.
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The expression is a difference of squares: x² - 3².
Thus, it factors as (x - 3)(x + 3).
