## The Lesson

A power can have an fraction raised to an exponent. This is a laws of exponents.

## Question

Use the law of exponents to find the power with the fraction below. # 1

Find the exponent of the power. In our example, the exponent is 2. # 2

Find the top number (called the numerator) of the fraction. In our example, the numerator is 3. # 3

Raise the number found in Step 2 (3) to the exponent found in Step 1 (2). This becomes the numerator of the answer. # 4

Find the bottom number (called the denominator) of the fraction. In our example, the denominator is 4. # 5

Raise the number found in Step 4 (4) to the exponent found in Step 1 (2). This becomes the denominator of the answer. We have used the law of exponents to find the power of a fraction. For the final steps, evaluate the powers in our fraction.

# 6

Evaluate the power on the top of the fraction. In our example, evaluate 32.
32 = 3 × 3 = 9

# 7

Evaluate the power on the bottom of the fraction. In our example, evaluate 42.
42 = 4 × 4 = 16

(34)2 is equal to 916. ## Understanding Finding a Power of a Fraction

Let us look at the rule for powers of a fraction: Firstly, let us look at what is to the left of the equals sign (=):
Let us look at the right hand side of the equals sign (=):
• The right hand side is a fraction.
• The top of the fraction is a power: 2n. It has a base of 2 with an exponent of n.
• The bottom of the fraction is a power: 3n. It has a base of 3 with an exponent of n.

## Lesson Slides

The slider below shows another real example of how to find the power of a fraction. Open the slider in a new tab
{"ft_lang_label":"__label__en","ft_lang_prob":0.8601655,"math_prob":0.983276,"size":1384,"snap":"2022-40-2023-06","text_gpt3_token_len":377,"char_repetition_ratio":0.18333334,"word_repetition_ratio":0.14545454,"special_character_ratio":0.2803468,"punctuation_ratio":0.118589744,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99979526,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-02-05T00:19:52Z\",\"WARC-Record-ID\":\"<urn:uuid:cefb36a5-737d-42d7-83cf-63103e7b9925>\",\"Content-Length\":\"18915\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:a7201830-6776-409c-9a45-46086f314a69>\",\"WARC-Concurrent-To\":\"<urn:uuid:0c6907d2-73bc-445c-82fc-629602834dbb>\",\"WARC-IP-Address\":\"69.90.25.69\",\"WARC-Target-URI\":\"https://www.mathematics-monster.com/lessons/how_to_find_a_power_of_a_fraction.html\",\"WARC-Payload-Digest\":\"sha1:ZBXH3F32B4IT6XZ75BR6IBD6OOXAI43D\",\"WARC-Block-Digest\":\"sha1:KJPVIAS2CGUUCGF2TMY35RWFBQBWEOXV\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-06/CC-MAIN-2023-06_segments_1674764500158.5_warc_CC-MAIN-20230205000727-20230205030727-00238.warc.gz\"}"}